Invariant two-jets and effective hyperbolicity for complements of two plane curves

Lei Hou, Pengchao Wang, Song-Yan Xie

Let $D=C_1+C_2\subset {\mathbb{P}}^2$ be a simple-normal-crossing union of smooth plane curves of degrees $1⩽d_1⩽d_2$. We prove an effective Second Main Theorem on a…